The Circle Game] is certainly much older than the Baby Boomers, being already a boys' standard in Middle School when I arrived in the 1960's. But what is the oldest known reference to it (or a reasonably clear antecedent, though it's hard to get much simpler)?
The game starts out when the Offensive Player creates a circle with their thumb and forefinger, not unlike an "A-Okay" signal, somewhere below his waist.
His goal is to trick another person into looking at his hand. If the Victim looks at the hand, he has lost the game, and is subsequently hit on the bicep with a closed fist, by the offensive player.
It is customary to playfully "wipe off the hit" after it is delivered. (Quick open hand brush on the bicep.)
I first encountered this game in 1966 or 1967 in Southern Ontario.
This is the game seen being played by a few Army and Navy Cadet spectators in last Saturday's (2019-12-14) Army-Navy football game making the circle symbol on national television (over announcer's right ear).
I have seen several mentions on Twitter over the weekend (no region information) about it being played in Middle and High School elsewhere in North America, and by groups of U.S. Marine enlisted men, over the past half century.
It is also sometimes called the "Made You Look Game" with the same rules.
Although in Middle School I saw it occasionally used as a means of bullying weaker students, by High School I saw it exclusively played by the jocks as a game of one-up-man-ship amongst themselves.
Here is the game being played on a Malcolm in the Middle episode (year unknown)